UP Police Constable · Bite-size lessons
Venn Diagrams
About 6 min · Mental Aptitude / IQ / Reasoning · English
Time worked out from the lesson's 439 words at 150 words a minute, plus a minute for each question.
Venn diagrams are graphical representations of logical relationships between different sets or groups. In the UP Police Constable exam, these questions test your ability to visualize how different categories overlap, intersect, or remain distinct. You may be given three terms (like "Teachers," "Women," "Doctors") and must identify which diagram correctly represents their relationship.
Key ideas
- Set representation: Each circle or closed figure represents a complete set or category of items/people with a common characteristic.
- Overlapping regions: When two circles overlap, the intersection represents items that belong to both categories simultaneously (e.g., "female doctors" in the overlap of "women" and "doctors").
- Subset relationships: When one circle is completely inside another, it indicates that all members of the smaller set are also members of the larger set (e.g., "roses" inside "flowers").
- Disjoint sets: Circles that don't touch represent mutually exclusive categories with no common members (e.g., "living things" and "non-living things").
- Three-set diagrams: Three categories create potential for various overlapping patterns — complete overlap, partial overlap, or no overlap.
Watch out for
- Wrong thinking: "Since all three are given, they must all connect somehow."
- Correct approach: Categories like "Males" and "Females" or "Living" and "Non-living" can never overlap — use separate circles.
- Wrong thinking: Drawing "Women" and "Teachers" as overlapping equals when one is not a subset of the other.
Quick reference
- Subset check: "Are ALL members of X also members of Y?" → If yes, draw X inside Y.
- Overlap check: "Can SOME members belong to both X and Y?" → If yes, make circles intersect.
- Disjoint check: "Is it IMPOSSIBLE for anything to be both X and Y?" → If yes, keep circles separate.
- Three-category strategy: Test all three pairwise relationships (A-B, B-C, A-C), then determine if central overlap exists.
- Common overlaps: Gender + Profession, Nationality + Profession, Age groups + Activities — these typically overlap.
Check yourself: 3 questions
1. Which of the following Venn diagrams best represents the relationship among 'Doctors', 'Engineers', and 'Human Beings'?
2. In a group of 100 people: 60 like tea, 50 like coffee, and 30 like both tea and coffee. How many people like neither tea nor coffee?
3. Which Venn diagram correctly represents the relationship among 'Fruits', 'Apples', and 'Bananas'?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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